If this victory occurs during the OTL Korean War, the effects it will have on American foreign policy would be interesting, to say the least. During the period in question, a paper known as
NSC 68 was being drafted by the State Department to come up with some suitable plan for dealing with the USSR. When it was finally completed in 1950, it argued that the basic foreign policy goal of the Kremlin was world hegemony, and that the ideal counter would be a vigorous application of containment policy, combined with plenty of increases in military spending. The outbreak of the Korean War and the spectre of further Soviet expansionism essentially convinced Truman, who had been trying to focus more on his domestic programs, to implement this plan, and it so became one of the founding documents of American Cold War policy.
If all of Korea goes red, I'd expect this mentality to grow even stronger. There's is a good chance that the cuts Eisenhower made to the military in the 1950s would be erased. He'd face too much opposition from a frightened public and Congress to do otherwise. While this allow some earlier successes in a Vietnam-analogue to occur, it does mean that the American economy will not be doing quite as well as in OTL, what with the incread military spending and all.
It's also rather interesting to consider what would happen to Korea. While things would be unpleasant, there's a real good chance that they won't get as bad as in OTL's North Korea, for the reason that this expanded DPRK would not be spending its time staring through a heavily defended border at an antagonistic neighbor. That's gotta cleave your military spending down a bundle right there. Furthermore, without the isolating effect of a nearby enemy, this DPRK might actually try to participate in foreign affairs as an equal nation, rather than as a mystical hermit kingdom where the rules do not apply.